On the irreducible representations of a finite semigroup
On the irreducible representations of a finite semigroup
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关于有限半群的不可约表示
DOI：
10.1090/s0002-9939-09-09857-8
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
B. Steinberg
中科院分区：
文献类型：
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作者：
O. Ganyushkin;V. Mazorchuk;B. Steinberg
Clifford，Munn和Ponizovskii的工作用极大子群的不可约表示来参数化有限半群的不可约表示。显式结构的不可约表示后来获得独立的罗兹和Zalcstein和Lallement和佩特里奇。所有这些方法都利用Rees定理刻画0-单半群直到同构。本文基于J.A.绿色，它使我们能够绕过0-单半群的理论。这种方法的新奇在于它适用于任何基环。
Work of Clifford, Munn and Ponizovskii parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Rees's theorem characterizing 0-simple semigroups up to isomorphism. Here we provide a short modern proof of the Clifford-Munn-Ponizovskii result based on a lemma of J. A. Green, which allows us to circumvent the theory of 0-simple semigroups. A novelty of this approach is that it works over any base ring.